A fully conservative second-order finite difference scheme for incompressible flow on non-uniform grids

A second-order-accurate finite difference discretization of the incompressible Navier-Stokes is presented that discretely conserves mass, momentum, and kinetic energy (in the inviscid limit) in space and time. The method is thus completely free of numerical dissipation and potentially well suited to the direct numerical simulation or large-eddy simulation of turbulent flow. The method uses a staggered arrangement of velocity and pressure on a structured Cartesian grid and retains its discrete conservation properties for both uniform and nonuniform gird spacing. The predicted conservation properties are confirmed by inviscid simulations on both uniform and nonuniform grids. The capability of the method to resolve turbulent flow is demonstrated by repeating the turbulent channel flow simulations of H. Choi and P. Moi